Foundations of GeometryOpen Court, 1971 - 226 pagine Along with the writings of Hilbert's friend and correspondent Frege, Hilbert's Grundlagen der Geometrie is the major prop that set the stage for Russell and Whitehead's Principia Mathematica. Hilbert presents a new axiomatization of geometry, the reduction of geometry to algebra, and introduces the distinction between mathematics and metamathematics, with a new theory of proof. This edition is translated from the tenth German edition, including all the improvements which Hilbert derived from his own reflections and the contributions of other writers. --Back cover. |
Sommario
Introduction | 2 |
The Consistence and the Mutual Independence of the Axioms | 29 |
Theory of Proportion | 44 |
Copyright | |
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angle theorem arbitrarily close Archimedean Axiom Archimedes assertion assumed asymptotic curve Axiom III axiom of parallels Cartesian geometry circle x closed Jordan curve commutative law complex numbers congruence axiom congruent mapping constructed converge coordinates corresponding deduced defined definition denoted Desargues equal equation equicomplementable equidecomposable Euclidean exists exterior angle theorem finite number following theorem formulated function Furthermore half rotation hence Hilbert hold inside kk interior K₁ K₂ law of multiplication lies Math midpoint neighborhood number circle number plane number set obtained parameters Pascal's Theorem perpendicular plane axioms plane geometry point of intersection polygon positive possible proof properties proved quadrilateral rational numbers real numbers region result right angles satisfied Section 13 segment arithmetic shown side simple polygon space geometry supplementary angles surface Theorem Theorem theory of proportion triangle ABC true circle true line valid vertex